Question

x dx/
[(x + 2){(x+1) ^(1/2)}]

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Answer 1

Answer:

2√(x+1) - 4 tan⁻¹ ( √x+1 ) + C

Step-by-step explanation:

(1) First we suppose

x + 1 = t²

Differentiating both sides with respect to x we get

( 1 + 0 ) dx = dt

=> dx = dt

Now , x+ 1 = t²

=> x = t² - 1

x + 1 = t²

=> t = √(x+1)

(2) In srcond step we put

x = t² -1 , dx = 2t dt and x + 1 = t²

(3) In fourth step we add and subtract 1 .

(4) In sixth step we break the fraction in to two fractions.

(5) In seventh step we apply formulee of intregation

∫ 1 dx = x + C

∫ dx / (x² + 1 ) = tan⁻¹x + C

(6) Now put t = √(x+1) in the last